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a) Ta thấy x=-2 thỏa mãn ĐKXĐ của B.
Thay x=-2 và B ta có :
\(B=\frac{2\cdot\left(-2\right)+1}{\left(-2\right)^2-1}=\frac{-3}{3}=-1\)
b) Rút gọn :
\(A=\frac{3x+1}{x^2-1}-\frac{x}{x-1}\)
\(=\frac{3x+1-x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{-x^2+2x+1}{\left(x-1\right)\left(x+1\right)}\)
Xấu nhỉ ??
Câu 1 ;
a) \(x^2-2x-15\)
= \(x^2-5x+3x-15\)
= \(x(x-5)+3(x-5)\)
= \((x+3).(x-5)\)
b) \(xy+\frac{1}{3}y-\frac{1}{4}x-\frac{1}{12}\)
= \((x+\frac{1}{3})y-\frac{1}{4}(x+\frac{1}{3})\)
= \((x-\frac{1}{4}).(x+\frac{1}{3})\)
Câu 2 :
\(A=\left(x+1\right)\left(x^2-x+1\right)+x-\left(x-1\right)\left(x^2+x+1\right)+1994\)
=> \(A=x^3+1+x-x^3+1+1994\)
=> \(A=1+x+1+1994\)
=> \(A=x+1996=-1995+1996=1\)
a, \(A=\left(\frac{1}{x-1}+\frac{x}{x^2-1}\right):\frac{2x+1}{x^2+2x+1}\)
\(=\left(\frac{1}{x-1}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)
\(=\left(\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)
\(=\frac{2x+1}{\left(x-1\right)\left(x+1\right)}.\frac{\left(x+1\right)^2}{2x+1}=\frac{x+1}{x-1}\)
b, Thay x = -2 ta được :
\(\frac{x+1}{x-1}=\frac{-2+1}{-2-1}=\frac{1}{3}\)
Vậy A nhận giá trị 1/3
\(A=\left(\frac{1}{x-1}+\frac{x}{x^2-1}\right)\div\frac{2x+1}{x^2+2x+1}\)
\(=\left(\frac{1}{x-1}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right)\div\frac{2x+1}{\left(x+1\right)^2}\)
\(=\left(\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right)\times\frac{\left(x+1\right)^2}{2x+1}\)
\(=\frac{2x+1}{\left(x-1\right)\left(x+1\right)}\times\frac{\left(x+1\right)^2}{2x+1}\)
\(=\frac{x+1}{x-1}\)
Với x = -2 (tmđk) => \(A=\frac{-2+1}{-2-1}=\frac{-1}{-3}=\frac{1}{3}\)
\(A=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(1+x+x^2\right)}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(x+1\right)}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{-x-1}{\left(1-x\right)\left(x+1\right)}-\frac{x}{\left(1-x\right)\left(x+1\right)}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\frac{-2x-1}{\left(1-x\right)\left(x+1\right)}:\frac{2x+1}{x^2+2x+1}\)
\(A=\frac{-\left(2x+1\right)}{\left(1-x\right)\left(x+1\right)}.\frac{\left(x+1\right)^2}{2x+1}\)
\(A=\frac{-1}{1-x}.\frac{x+1}{1}\)
\(A=\frac{-x-1}{1-x}\)